If 3^x/(1 - 3^x) = 1/3
then the value of 27^x/(1- 27^x) is ?
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3^x/1-3^x=1/3 => 3^x×3=1-3^x
=> 3^(x+1)=1-3^x
=> 3^x(3+1)=1
=> 3^x= 1/4
now cubing on both sides we get ,
=>3^3x=[1/4]^3
=>27^x=1/64--------------(1) ,,,,,substitute (1) in 27^x/1-27^x = (1/64)/(1-1/64)=(1/64)/(63/64)
=>1/63
=> 3^(x+1)=1-3^x
=> 3^x(3+1)=1
=> 3^x= 1/4
now cubing on both sides we get ,
=>3^3x=[1/4]^3
=>27^x=1/64--------------(1) ,,,,,substitute (1) in 27^x/1-27^x = (1/64)/(1-1/64)=(1/64)/(63/64)
=>1/63
mysticd:
excellent work
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